A261614 Numbers that are neither prime (A000040) nor practical (A005153).

9, 10, 14, 15, 21, 22, 25, 26, 27, 33, 34, 35, 38, 39, 44, 45, 46, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 68, 69, 70, 74, 75, 76, 77, 81, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 110, 111

Offset: 1

Author

Frank M Jackson, Nov 18 2015

Keywords

• nonn

Examples

			a(5)=21 and it is neither prime nor practical. It is the 5th such occurrence.
		

Crossrefs

Cf. A000040, A005153, A225223.

Programs

Mathematica

PracticalQ[n_] := Module[{f, p, e, prod = 1, ok = True}, If[n<1||(n>1&&OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e}=Transpose[f]; Do[If[p[[i]]>1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; Select[Range[1, 1000], ! PracticalQ[#] && ! PrimeQ[#] &] (* using T. D. Noe's program A005153 *)

PARI

isok(n) = bittest(n, 0) && return(n==1); my(P=1); n && !for(i=2, #n=factor(n)~, n[1, i]>1+(P*=sigma(n[1, i-1]^n[2, i-1])) && return) ;
for(n=1, 200, if(!isok(n) && !isprime(n), print1(n, ", "))) \\ Altug Alkan, Nov 19 2015